Question

Can someone please help me with this ??

Answer 1

Answer:  d =  -16 .
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Explanation:
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Given:  0.2 (d − 6) = 0.3d + 5 − 3 + 0.1 d  ; Solve for "d" ;
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→ Note the distributive property of multiplication:
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            a (b + c) = ab + ac ;
            a (b − c) = ab − ac ;
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As such, we can expand the left-hand side of the question:
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→ 0.2 (d − 6) = (0.2 *d) − (0.2 *6)  = 0.2 d − 1.2; 
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And rewrite the entire equation: 
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→ 0.2 d − 1.2 = 0.3d + 5 − 3 + 0.1 d ;
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→ Let us multiply the ENTIRE equation (both sides) by "10"; to get rid of the decimals:
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   → 10 * {0.2 d − 1.2 = 0.3d + 5 − 3 + 0.1 d} ;
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   →  2d − 12 = 3d + 50 − 30 + 1d ;  
   
→ Combine the "like terms",  +3d , +1d  ; to get 4d; on the 'right-hand side' of the equation ; and rewrite:

 →  2d − 12 = 4d + 50 − 30 ;  

 →  Now add "12"; and subtract "2d" from EACH SIDE of the equation; 

 →  2d − 12 + 12 − 2d= 4d + 50 − 30 + 12 − 2d ;

→  0 = 2d + 32 ;  ↔  2d + 32 = 0 ; 

                           → Subtract "32" from each side of the equation:
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          → 2d + 32 − 32 = 0 − 32 ;
    
          → 2d  = - 32
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→ Now, divide EACH side of the equation by "2" ; to isolate "d" on ONE side of the equation; and to solve for "d" ;
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         →   2d / 2  =  - 32 / 2 ; 
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         →         d  =  - 16  ;  which is our answer.
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     Let us check our answer by plugging this value for "d" in the original equation to see if the equation holds true when "d = -16" ; 
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               →  0.2 (d − 6) = 0.3d + 5 − 3 + 0.1 d ;
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    →  Let us start with the "left-hand side".
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         → 0.2 (d − 6) ;  ↔ 0.2*(-16 − 6) ; ↔ 0.2*(-22) = -4.4.
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When "d" = -16 in the right-hand side of the equation,
                                                          is the result, "-4.4" ???
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   →  0.3d + 5 − 3 + 0.1 d = ? -4.4 ???
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    →  (0.3 * -16)  + 5 − 3 + (0.1 * -16) =? -4.4???
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    →  (-4.8) + 5 − 3 + (-1.6)  = ? -4.4????
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   →  (-4.8) + 5 − 3  − (1.6)  = ? -4.4????

→ -4.4 =? -4.4??? Yes!!!
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